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Simulating a continous distribution

  1. Oct 22, 2013 #1
    Say we want a set of random values that are distributed according to some distribution function f(x).

    A common way to accomplish that is to find the cumulative distribution function F(x) for the distribution and then solve for x according to

    F(x) = Y

    x = F'(Y)

    Then x will be distributed with the original distribution function, if F'(Y) is fed with random values Y ranging from 0-1.

    I'm currently trying to do that with a weibull distribution

    f(x) = a*b*xb-1*e-a*b*x^b

    where F(x) should be

    F(x) = e-a - e-a*x^b

    when solving for x in F(x) I however get

    x = ( - ln(e-a - Y)/a)1/b

    When Y> e-a there are no real solutions. Is there a way to get around this? Have I done something wrong?
     
  2. jcsd
  3. Oct 22, 2013 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Your F(x) can't be right. F(∞) should be 1.
     
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